Abstract: Many problems in control and optimization require the treatment of systems in which continuous dynamics and discrete events coexist. This talk presents a survey on some of our recent work on such systems. In the setup, the discrete event is formulated as a random process with a finite state space, and the continuous component is the solution of a deterministic or stochastic differential equation. Seemingly similar to the systems without switching, the processes have a number of features that are distinctly different from processes without switching. After providing motivational examples arising from wireless communications, finance, singular perturbed Markovian systems, manufacturing, and consensus controls, we present necessary and sufficient conditions for the existence of unique invariant measure, stability, stabilization, and numerical solutions of control and game problems.